Bioinspired Machine Learning for Distributed Confidential MultiPortfolio Selection Problem
Abstract
:1. Introduction
2. Problem Formulation
2.1. Building Blocks of Portfolio Selection
2.1.1. Expected Return
2.1.2. Risk
2.1.3. Total Investment
2.1.4. Total Transaction Cost
2.1.5. Cardinality Constraint
2.2. Portfolio Selection Models
2.2.1. MeanVariance Model
2.2.2. Efficient Frontier Model
2.2.3. Sharpe Ratio Model
3. Distributed Beetle Antennae Search (DBAS)
3.1. BAS Formulation and Algorithm
Algorithm 1 BAS Algorithm. 

3.2. DBAS Formulation and Algorithm
3.2.1. DBAS Updating Criteria
Algorithm 2 DBAS Algorithm. 

3.2.2. DBAS Privacy Policy
4. Simulation Results
4.1. Stock Data
 Software: MATLAB;
 System: MacBook Pro;
 Processor: 2.2 GHz;
 Cores: 6–Core Intel Core i7;
 Memory: 6 GB 2400 MHz DDR4;
 Graphics: Radeon Pro 555X 4 GB.
4.2. Three Portfolios of Five Stock Companies
4.3. Three Portfolios of 10 Stock Companies
4.4. Three Portfolios of 15 Stock Companies
4.5. Three Portfolios of 20 Stock Companies
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Name  Notation  Values (Default) 

Antennae Length  d  $0.9$ 
Step Size  $\tau $  $0.9$ 
Personal Antennae Length  ${d}_{1}$  $0.9$ 
Global Antennae Length  ${d}_{2}$  $0.9$ 
Step Multiplier  $\eta $  $0.99$ 
Companies 1–5  GOOGL  MSFT  AMZN  FB  IBM 

Companies 6–10  A  AA  AAU  AABA  AAC 
Companies 11–15  AADR  AAL  AAMC  AAME  AAN 
Companies 16–20  NCA  NCI  QAT  QD  CODI 
Companies 20–25  EMR  EMXC  FET  FC  ABBV 
Companies: 5  Companies: 10  

Portfolio 1  Portfolio 2  Portfolio 3  Portfolio 1  Portfolio 2  Portfolio 3  
n  5  5  5  7  8  9 
${G}_{best}$  ${10}^{7}$  ${10}^{7}$  ${10}^{7}$  ${10}^{6}$  ${10}^{6}$  ${10}^{6}$ 
${\mathbf{P}}_{\mathbf{best}}$  ${10}^{6}$  ${10}^{7}$  ${10}^{6}$  ${10}^{6}$  ${10}^{6}$  ${10}^{4}$ 
$SR$  $72.348$  $24.804$  $39.582$  $9.108$  $5.319$  $3.151$ 
$(\mathbf{1}+\mathbf{\alpha})E=1$  $1.116$  $1.179$  $1.065$  $1.153$  $1.140$  $0.964$ 
DBAS:  
$\eta $  $0.900$  $0.900$  
$d={d}_{1}={d}_{2}$  $0.999$  $0.900$  
$\tau $  $0.900$  $0.900$  
sgn  $[1,1]$  $[1,1]$  
Some Additional Parameters:  
T  500  500  
D  3  3  
K  5  5  
$\mathbf{H}(E,\mathbf{\sigma})$ Eval.  4500  4500  
Companies: 15  Companies: 20  
Portfolio 1  Portfolio 2  Portfolio 3  Portfolio 1  Portfolio 2  Portfolio 3  
n  15  12  10  15  20  18 
${G}_{best}$  ${10}^{4}$  ${10}^{4}$  ${10}^{4}$  ${10}^{7}$  ${10}^{7}$  ${10}^{7}$ 
${\mathbf{P}}_{\mathbf{best}}$  ${10}^{4}$  $0.020$  $0.001$  ${10}^{7}$  ${10}^{7}$  ${10}^{6}$ 
$SR$  $7.088$  $3.667$  $4.667$  $58.71$  $21.56$  $191.6$ 
$(\mathbf{1}+\mathbf{\alpha})E=1$  $0.930$  $1.088$  $1.103$  $0.9893$  $1.136$  $1.021$ 
DBAS:  
$\eta $  $0.850$  $0.950$  
$d={d}_{1}={d}_{2}$  $0.900$  $0.900$  
$\tau $  $0.850$  $0.850$  
sgn  $[1,1]$  $[1,1]$  
Some Additional Parameters:  
T  500  500  
D  3  3  
K  5  5  
$\mathbf{H}(E,\mathbf{\sigma})$ Eval.  4500  4500 
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Khan, A.T.; Cao, X.; Liao, B.; Francis, A. Bioinspired Machine Learning for Distributed Confidential MultiPortfolio Selection Problem. Biomimetics 2022, 7, 124. https://doi.org/10.3390/biomimetics7030124
Khan AT, Cao X, Liao B, Francis A. Bioinspired Machine Learning for Distributed Confidential MultiPortfolio Selection Problem. Biomimetics. 2022; 7(3):124. https://doi.org/10.3390/biomimetics7030124
Chicago/Turabian StyleKhan, Ameer Tamoor, Xinwei Cao, Bolin Liao, and Adam Francis. 2022. "Bioinspired Machine Learning for Distributed Confidential MultiPortfolio Selection Problem" Biomimetics 7, no. 3: 124. https://doi.org/10.3390/biomimetics7030124